Isochron is an equal-age line for measured present-day parent and daughter isotopic ratios of co-genetic minerals and rocks plotted on an isochron diagram. Isochrons provide ages and initial isotopic ratios of the samples useful to understand their geological evolution. However, the statistical criterion used to declare an isochron cannot guarantee the co-genesis of the samples. During eight decades of application of the isochron method of dating, a geological criterion did not emerge because the process of isotopic resetting in metamorphic rocks has not been investigated in its real perspective. Thus, isochron rotation in isochron diagrams was envisaged during isotopic resetting though incompletely reset whole-rocks and minerals suggest isochron translation. In such rocks, an isochron appears to have moved or translated parallel to itself on the isochron diagram during partial resetting enveloping a data scatter between sub-parallel lines. Here isochron translation has been confirmed using computer simulations of whole-rock isotopic resetting. Isochron translation proceeding in three distinct stages establishes a Field Gradient of Initial Ratios (FGIR) in the third stage, characteristic of co-genetic samples, useful as a geological criterion to declare an isochron. Isochron translation is a fingerprint of layer arrangement, layer thickness and isotopic composition of rocks, and enables (a) derivation of accurate isotopic ages, (b) re-evaluation of statistically rejected data, (c) resolving isotopic heterogeneities in the earth’s crust and mantle, (d) evaluation of model ages and mineral ages.